. The price-demand equation and the cost function for the production of honey is given, respectively, by x = 5,000 - 100p and C(x) = 2,500 + 4x+ 0.01x2 where x is the number of bottles that can be sold at a price of $p per bottle and C(x) is the total cost (in dollars) of producing x bottles.

a) Express the price p as a function of the demand x, and find the domain of this function.

b) Find the marginal cost.

c) Find the revenue function and state its domain.

d) Find the marginal revenue.

e) Find R(2,000) and R(3,000) and interpret these quantities.

f) Find the profit function in terms of x.

g) Find the marginal profit.

h) Find P(1,000) and P(1,500) and interpret these quantities.